It is not part of the keyboard, no. The TouchBar is a separat OLED touch screen. It is meant to stay on even without keyboard backlight. An obvious example of this, is that you can turn off the backlight on the keyboard using the TouchBar, and so to turn it on again, you'd obviously need the TouchBar.
I think at the present moment, no, but it'll probably be added in a future software release. I don't have one to check, but I'd advice looking under Energy Saver in System Preferences. There may also be Terminal commands that let you do it, but I do not know
It's up to the app devs to update their apps accordingly. For example, VLC needs to update their app so when a movie is playing the touch bar dims or turns off until touched. I wrote to them and requested they do it. LOL